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lfunc_lfunctions • Show schema
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{'Lhash': '1629171730949668637826634576710', 'a10': 1, 'a2': 1, 'a3': -3, 'a4': 1, 'a5': 1, 'a6': -3, 'a7': 1, 'a8': 1, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.63329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1, -1]], [7, [1, -1]], [11, [1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '8470.1', 'coefficient_field': '1.1.1.1', 'conductor': 8470, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[1, -1], [1, 3, 3], [1, -1], [1, -1], [1], [1, -1, 13], [1, 0, 17], [1, 7, 19], [1, -1, 23], [1, -8, 29], [1, 4, 31], [1, -2, 37], [1, 6, 41], [1, 6, 43], [1, 12, 47], [1, 12, 53], [1, -3, 59], [1, 6, 61], [1, -8, 67], [1, 8, 71], [1, -16, 73], [1, 9, 79], [1, 13, 83], [1, -6, 89], [1, 8, 97], [1, -15, 101], [1, -6, 103], [1, -2, 107], [1, 0, 109], [1, 9, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 3, 3], 1]], [[[1, -1], 1]], [[[1, -1], 1]], [1], [[[1, -1, 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-1.5297977445328246, -0.7281552548124168, -0.021486472079848735, 0.5787454828765085, 1.0648805385824356, 1.433159714193585, 1.6836906317333253, 1.8202841560825314, 1.85017030914364], 'positive_zeros': ['1.28518988643743829666897335446888', '2.02334425857573674783246704259818', '3.23257720808383244286451436629701', '4.26539803244593129222904142714486', '4.82125760783752219268403820523352', '5.26781262700688478211136983436226', '6.14370984861820886613838187942922', '6.45933331757336568791492477541962', '6.97367089659976974176485816482054'], 'prelabel': '2-8470-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.223946164222168, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1396816836056058940, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28518988643743829666897335447', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02334425857573674783246704260', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23257720808383244286451436630', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.63329051202452, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 8470, 'conductor_radical': 770, 'degree': 2, 'dirichlet_coefficients': [1, 1, -3, 1, 1, -3, 1, 1, 6, 1, 0, -3, 1, 1, -3, 1, 0, 6, -7, 1, -3, 0, 1, -3, 1, 1, -9, 1, 8, -3, -4, 1, 0, 0, 1, 6, 2, -7, -3, 1, -6, -3, -6, 0, 6, 1, -12, -3, 1, 1, 0, 1, -12, -9, 0, 1, 21, 8, 3, -3, -6, -4, 6, 1, 1, 0, 8, 0, -3, 1, -8, 6, 16, 2, -3, -7, 0, -3, -9, 1, 9, -6, -13, -3, 0, -6, -24, 0, 6, 6, 1, 1, 12, -12, -7, -3, -8, 1, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, -1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 7, 19], 'euler2': [1, -1, 0], 'euler23': [1, -1, 23], 'euler29': [1, -8, 29], 'euler3': [1, 3, 3], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 6, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, 12, 53], 'euler59': [1, -3, 59], 'euler61': [1, 6, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -16, 73], 'euler79': [1, 9, 79], 'euler83': [1, 13, 83], 'euler89': [1, -6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, -1, 0], [1, 3, 3], [1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -1, 13], [1, 0, 17], [1, 7, 19], [1, -1, 23], [1, -8, 29], [1, 4, 31], [1, -2, 37], [1, 6, 41], [1, 6, 43], [1, 12, 47], [1, 12, 53], [1, -3, 59], [1, 6, 61], [1, -8, 67], [1, 8, 71], [1, -16, 73], [1, 9, 79], [1, 13, 83], [1, -6, 89], [1, 8, 97]], 'index': 171, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/8470/q', 'ModularForm/GL2/Q/holomorphic/8470/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/8470/2/a/q'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-8470-1.1-c1-0-171', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8470-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.223946164222168, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1396816836056058940, 'z1': {'__RealLiteral__': 0, 'data': '1.28518988643743829666897335447', 'prec': 103}}
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lfunc_instances • Show schema
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id: 22627088
{'Lhash': '1629171730949668637826634576710', 'Lhash_array': ['1629171730949668637826634576710'], 'label': '2-8470-1.1-c1-0-171', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8470/2/a/q'}
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id: 24584194
{'Lhash': '1629171730949668637826634576710', 'Lhash_array': ['1629171730949668637826634576710'], 'label': '2-8470-1.1-c1-0-171', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8470/2/a/q/1/1'}
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id: 22474
{'Lhash': '1396816836056058940', 'Lhash_array': ['1396816836056058940'], 'label': '2-8470-1.1-c1-0-171', 'type': 'ECQ', 'url': 'EllipticCurve/Q/8470/q'}